Method to Determine Individualized Insulin Sensitivity and Optimal Insulin Dose by Linear Regression

ABSTRACT

This invention relates to a method and a device for predicting the glucose concentration of a subject and recommending therapeutic action. The responses of the user&#39;s glucose to administered doses of insulin, dietary carbohydrates, and other factors influencing glucose concentration are measured individually for a given user. Once these responses are learned as a function of time, the method and device can receive information about the factors which have been recently or will soon be administered and can recommend which other factors should also be administered.

1 CROSS-REFERENCE TO RELATED APPLICATIONS AND STATEMENT REGARDING SPONSORED RESEARCH

This application claims the benefit of Patent Application Ser. No. 62/083,191, titled Method to Determine Individualized Insulin Sensitivity and Optimal Insulin Dose by Linear Regression, filed Nov. 22, 2014 by the present inventors, which is incorporated by reference. This invention was not made with any government support and the government has no rights in this invention.

2 Description

2.1 Field of the Invention

The present invention relates to a method for predicting the glucose concentration of a subject and recommending therapeutic action.

2.2 Background

In the United States, approximately three million people have type 1 diabetes [1]. To treat their condition, these patients depend either on multiple daily injections (MDI) of insulin or continuous subcutaneous insulin injection (CSII) by insulin pumps. Another 26 million people in the United States suffer from type 2 diabetes, many of whom become insulin dependent. In total, nearly six million Americans depend on insulin [2]. For these patients, choosing the correct dose and type of insulin to take, and when to take it, remains a significant challenge. The goal of an insulin regimen is to maintain blood glucose concentration within a narrow range. Chronically high glucose levels, hyperglycemia, leads to severe health problems and premature death. Acute low glucose levels, hypoglycemia, can cause fainting, seizures, and death. Patients on MDI maintain a healthy glucose level by typically taking five to ten injections per day. These may include injection of a long-acting form of insulin before going to sleep and/or after waking, as well as short-acting insulin injections both before and after every meal and snack, with those following meals chosen to correct for prior insufficient doses. In order to make informed dosage decisions, most diabetics today monitor their blood glucose with small blood draws from a finger prick before each injection. An increasing number of diabetics also monitor their glucose using a continuous glucose monitor (CGM), which provides glucose readings with much higher frequency, commonly around once every five minutes. Although it has already been appreciated that this high frequency data can be used to alert users to problematic glucose levels as they arise, the wealth of data provided by these machines has, so far, been underutilized for the challenge of determining optimal insulin doses.

An “artificial pancreas” is a heavily researched future treatment device for diabetes that uses a closed loop between a CGM and an insulin pump. Given frequent, accurate readings from a CGM, the insulin pump should be able to determine, without human intervention, how much insulin to give. This will require the development of an algorithm that can precisely calculate the response of blood glucose to insulin.

Previous inventions in the field of glucose prediction have used the time-series of glucose over a narrow window in the recent past, possibly around 30 minutes, to predict glucose over a similar time frame in the future, without directly accounting for external factors like insulin, dietary carbohydrates, and exercise. The previous inventions also often focus on making universal predictions of insulin response that are not individualized to each patient and they predict a single, time-integrated response rather than response as a function of time.

The patent application “Universal models for predicting glucose concentration in humans” [3], “utilizes similarities in the short-term (30-minute or less) dynamics of glucose regulation in different diabetic individuals to develop a single, universal autoregressive (AR) model for predicting future glucose levels across different patients.” This patent does not account for external factors that cause changes in glucose or attempt to learn individualized models for different patients. Similarly, the patent application, “Neural network for glucose therapy recommendation” [4] uses recent glucose trends to predict future glucose trends, with the model trained on data from multiple patients rather than individualized. The patent application, “Medical device for predicting a user's future glycemic state” [5] uses CGM data to predict future glycemic state using a Hidden Markov Model and not linear regression. This method does not use information other than the time series of glucose before the moment of prediction to predict future glucose.

The patent application, “System for determining insulin dose using carbohydrate to insulin ratio and insulin sensitivity factor” [6] is a method for finding individualized carbohydrate-to-insulin ratios (CIRs) and insulin sensitivity factors (ISFs). At its greatest level of detail, that method gives the integrated effect of a unit of insulin or a carbohydrate on a users glucose concentration, and not the effect as a function of time. That method also does not use linear regression.

The patent application, “Glucose predictor based on regularization networks with adaptively chosen kernels and regularization parameters” [7] describes a method for predicting glucose based on data sets that are sparsely sampled in time, which does not make use of the glucose time series data made available by CGMs and the insulin time series data made available by insulin pumps. That method uses regularization networks with adaptively chosen kernels and regularization parameters and not linear regression.

3 SUMMARY OF THE INVENTION

This patent is for a linear regression-based method to learn a user's blood glucose response to short-acting insulin, long-acting insulin, dietary carbohydrates, and lifestyle factors such as exercise. This method learns a unique response for each user. The calculated response curve is a function of time, not merely the total time-integrated effect of 1 unit of a given factor. After obtaining these response functions, in a second step, this method determines optimal insulin dosages in response to the user's relevant activities. This separate step allows the method to assign an asymmetrical cost function for hyperglycemia and hypoglycemia. This asymmetry is necessary because a positive fluctuation that results in only mild hyperglycemia and no immediate problems could, if only the sign of the fluctuation were reversed, cause severe hypoglycemia and death: Including this information in the same step as learning the user's response to insulin and carbohydrates would distort the user's true response. From the time series of a given user's glucose, insulin, exercise, and carbohydrate intake, the method learns the optimal dose and time of long-acting insulin, the optimal ratio of short-acting insulin to dietary carbohydrates, the optimal correction dose of short-acting insulin for hyperglycemia, and the typical effect of exercise on the user's blood glucose.

The two steps, learning the user's response curves and suggesting the optimal insulin dose, can be decoupled. Once the time dependent response curves are calculated, they can be integrated to determine the cumulative effect of each kind of insulin and dietary carbohydrates. The insulin:carb ratio can then be calculated as the total effect of 1 unit of insulin divided by the total effect of 1 carbohydrate. Alternatively, clinically averaged response functions from many patients, in combination with the user's weight, can be used as an approximate input for the second step, determining the optimal insulin dose.

4 BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram depicting the input and output to the two stages of the process of determining individualized insulin sensitivity and optimal insulin dose.

5 DESCRIPTION OF EXEMPLARY EMBODIMENTS

Step 1 of the method linearly regresses changes in glucose over possibly overlapping time intervals onto the following equation:

${\Delta \; g_{i,j}} = {{\left( {{E\; G\; P_{0}} - {p*g_{i}}} \right)*\Delta \; t_{i,j}} + {R\; G\; C} + {\sum\limits_{j = 1}^{N_{short}}\; {\theta_{{short},j}S_{j}}} + {\sum\limits_{j = 1}^{N_{long}}\; {\theta_{{long},j}L_{j}}} + {\sum\limits_{j = 1}^{N_{carb}}\; {\theta_{{carb},j}C_{j}}}}$

where,

-   g_(i) is the i^(th) glucose measurement in time, -   Δg_(i,j)=g_(i+j)−g_(i), -   Δt_(i,j)=t_(i+j)−t_(i), -   EGP₀ is endogenous glucose production extrapolated to 0 glucose, a     fit parameter; p is suppression of endogenous glucose production, a     fitting parameter; -   RGC=A(g_(i)−g_(RGC)) if g>g_(RGC) and RGC=0 otherwise, represents     renal glucose clearance where A and g_(RGC)—the renal glucose     clearance threshold—are fit parameters; -   θ_(short,j) are responses to short-acting insulin doses S_(j)     administered j time periods before t_(i), where each time period     could be 30 to 60 minutes, are fit parameters; -   θ_(long,j) are responses to long-acting insulin doses L_(j)     administered j time periods before t_(i), where each time period     could be 30 to 60 minutes, are fit parameters; and -   θ_(carb,j) are responses to dietary carbohydrates C_(j) administered     j time periods before t_(i), where each time period could be 15 to     60 minutes, are fit parameters.

As another example linear-fit form, step 1 of the method could fit glucose changes to the following equation:

${\Delta \; g_{i,j}} = {{\left( {{E\; G\; P_{0}} - {p*g_{i}}} \right)*\Delta \; t_{i,j}} + {R\; G\; C} + {\sum\limits_{j = 1}^{N_{short}}\; {\sum\limits_{k = 0}^{d_{short}}{{\theta_{{short},k}\left( {t_{i} - t_{{short},j}} \right)}^{k}S_{j}}}} + {\sum\limits_{j = 1}^{N_{long}}\; {\sum\limits_{k = 0}^{d_{long}}{{\theta_{{long},k}\left( {t_{i} - t_{{long},j}} \right)}^{k}L_{j}}}} + {\sum\limits_{j = 1}^{N_{carb}}{\sum\limits_{k = 0}^{d_{carb}}\; {{\theta_{{carb},k}\left( {t_{i} - t_{{carb},j}} \right)}^{k}C_{j}}}}}$

where,

-   S_(j) are doses of short-acting insulin taken within some timeframe     of t_(i), possibly 6 hours; -   L_(j) are doses of long-acting insulin taken within some timeframe     of t_(i), possibly 24 hours; -   C_(j) are dietary carbohydrates eaten within some timeframe of     t_(i), possibly 3 hours;     and d_(short), d_(long), d_(carb) are the degrees of polynomial     response functions.

For any linear-fit form, the length of the time periods for the response curves in step 1 is chosen such that the rate of change of glucose to that factor has an insignificant fluctuation over the time period. The number of time periods to look back from each g_(i)—which could be different for each factor—is chosen such that the number of periods multiplied by the length of each period is longer than the time for the insulin, carbohydrate, or exercise to clear the body. Endogeneous glucose production could also be set as a separate factor for different times of day, possibly blocks of one to six hours.

In step 2, the method could use the response functions learned in step 1 to suggest appropriate insulin doses. The output could be carbohydrate ratios, correction doses, and long-acting insulin doses for a user on MDI, or basal and bolus rates for CSII, to be programmed manually in an existing open-loop pump system or to be set automatically in a future, closed-loop artificial pancreas. The method takes the actual time series of food and exercise and combines them with the times, but not the sizes, of actual insulin doses, as well as the response functions to these factors learned in step 1. The method then calculates optimal insulin doses for each relevant event, where the ideal dose is the one that minimizes a cost function that penalizes hyperglycemia and hypoglycemia. The cost function for excursions outside the optimal glucose range could be asymmetrical in order to avoid hypoglycemia more strongly than hyperglycemia. By then averaging over dose size per carbohydrate at each meal, the method can be used to suggest a best insulin:carb ratio. Similarly, by averaging over the ideal correction dose for a given glucose level at each episode of hyperglycemia, the method can suggest the proper correction dose for different levels of hyperglycemia. Step 2 will also assume that a fixed amount of long-acting insulin is taken each day, and it can suggest its ideal dose and time of application.

REFERENCES

-   [1] JDRF, Statistics: JDRF and Diabetes,     http://jdrf.org/about-jdrf/fact-sheets/jdrf-and-diabetes-statistics/,     2014 -   [2] Centers for Disease Control and Prevention, Number (in Millions)     of Adults with Diabetes by Diabetes Medication Status, United     States, 1997-2011,     http://www.cdc.gov/diabetes/statistics/meduse/fig1.htm, 2013 -   [3] US20110160555, Filed Jul. 31, 2009, Published Feb. 4, 2010,     Government Of The United States As Represented By The Secretary Of     The Army, Universal models for predicting glucose concentration in     humans -   [4] U.S. Pat. No. 9,076,107, Filed Aug. 14, 2009, Published Jun. 24,     2014, Brent D. Cameron, Scott M. Pappada, Neural network for glucose     therapy recommendation -   [5] U.S. Pat. No. 7,695,434, Filed Oct. 19, 2007, Published Apr. 23,     2009, Michael Malecha, Medical device for predicting a user's future     glycemic state -   [6] US20050192494, Filed Mar. 1, 2004, Published Jul. 29, 2008,     Barry H. Ginsberg, System for determining insulin dose using     carbohydrate to insulin ratio and insulin sensitivity factor -   [7] US20140073892, Filed Apr. 20, 2012, Published Oct. 26, 2012,     Samuel McKennoch, Sergei Pereverzyev, Jette Randlov, Sivananthan     Sampath, Glucose predictor based on regularization networks with     adaptively chosen kernels and regularization parameters 

1. A medical device for measuring the change in a user's glycemic state in response to outside forces comprising a) a memory module; b) a processor module; c) an electronic communication module; and d) wherein the memory module is configured to receive and store a plurality of glucose concentrations as a function of time that were generated by the user's use of a continuous glucose monitor, and e) wherein the memory module is configured to receive and store the amount and type of insulin the user injected at the time it was injected, the amount of carbohydrates the user consumed at the time they were consumed, and doses of other factors that may affect glucose, and f) wherein the processor module is configured to: i. derive rates of change in the user's glucose concentration as a function of time from the plurality of glucose concentrations stored in the memory module; ii. derive a glucose response as a function of time that is a fit to the plurality of glucose concentrations, insulin doses, carbohydrate doses, and doses of other factors that may affect glucose as a function of time stored in the memory module, the fit being based on a mathematical model; iii. integrate the glucose response as a function of time to obtain the user's total glucose response to insulin doses, carbohydrate does, and doses of other factors that may affect glucose, and g) wherein the electronic communication module is configured to transfer the glucose response functions and their integrated values to a display module or to another medical device, possibly an insulin pump.
 2. A medical device for recommending the type and size of a user's insulin dose comprising a) a memory module; b) a processor module; and c) an electronic communication module d) wherein the memory module is configured to receive and store i. a confidence interval of the response of the user's glucose concentration to insulin doses, carbohydrates doses, and doses of other factors that may affect glucose, and ii. a record of insulin doses previously administered to the user as a function of time, iii. a record of carbohydrates consumed and doses of other factors that may affect glucose administered to the user as a function of time, e) wherein the processor module is configured to use a mathematical model to calculate an optimal dose of insulin to be taken by the user in real time by projecting a time series of future glucose concentrations over a predetermined amount of time and minimizing an error function that penalizes deviations away from a predetermined ideal glucose level f) wherein the electronic communication module is configured to send the optimal dose of insulin to a display module or to another medical device, possibly an insulin pump.
 3. The medical device of claim 1 wherein the mathematical model is a linear regression where the dependent variable is change in glucose over possibly overlapping time intervals and the independent variables are doses of insulin, dietary carbohydrates, and other factors that may affect glucose summed over windows of time prior to the time window during which the glucose change is being regressed.
 4. The medical device of claim 1 wherein the mathematical model is a linear regression where the dependent variable is change in glucose over possibly overlapping time intervals and the independent variables are doses of insulin, dietary carbohydrates, and other factors that may affect glucose multiplied by a polynomial dependent on the time delay between when the dose was administered and when the glucose response is being measured.
 5. The medical device of claim 2 wherein the mathematical model's error function penalizes deviations of the glucose concentration below the predetermined ideal glucose level more than deviations of the glucose concentration above the predetermined ideal glucose level, whereby a glucose concentration below the ideal level is made less likely.
 6. The medical device of claim 1 wherein the doses of other factors that may affect glucose include duration of exercise engaged in by the user.
 7. The medical device of claim 2 wherein the doses of other factors that may affect glucose include duration of exercise engaged in by the user. 